Nuprl Lemma : oal_neg_keys_invar
∀a:PosetSig. ∀b:GrpSig. ∀ps:(|a| × |b|) List. (map(λz.(fst(z));--ps) = map(λz.(fst(z));ps) ∈ (|a| List))
Proof
Definitions occuring in Statement :
oal_neg: --ps,
map: map(f;as),
list: T List,
pi1: fst(t),
all: ∀x:A. B[x],
lambda: λx.A[x],
product: x:A × B[x],
equal: s = t ∈ T,
grp_car: |g|,
grp_sig: GrpSig,
set_car: |p|,
poset_sig: PosetSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
oal_neg: --ps,
member: t ∈ T,
uall: ∀[x:A]. B[x],
top: Top,
compose: f o g,
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list_wf,
set_car_wf,
grp_car_wf,
grp_sig_wf,
poset_sig_wf,
map_map,
map_wf,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality
Latex:
\mforall{}a:PosetSig. \mforall{}b:GrpSig. \mforall{}ps:(|a| \mtimes{} |b|) List. (map(\mlambda{}z.(fst(z));--ps) = map(\mlambda{}z.(fst(z));ps))
Date html generated:
2016_05_16-AM-08_19_04
Last ObjectModification:
2015_12_28-PM-06_26_26
Theory : polynom_2
Home
Index